Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#21819 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C23×C17 | C23×C4 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
1042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,30)(25,28)(26,29)(27,32)(31,36)(33,35)(34,37)(38,39,41,44,42,45,48,51)(40,43,47,50,46,49,52,53);(22,24,26,32)(23,27,29,30)(25,33,34,31)(28,36,37,35);(19,21)(22,25,26,34)(23,28,29,37)(24,31,32,33)(27,35,30,36)(38,40)(39,43)(41,47)(42,46)(44,50)(45,49)(48,52)(51,53);(23,29)(27,30)(28,37)(35,36)(40,46)(43,49)(47,52)(50,53)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14807);